Question

Given that the meaning of a rational exponent can be connected to the meaning of a root, how can you rewrite 5–√3 using a rational exponent?(1 point) Pick one of the answer below
Responses

5^3
5 cubed

5 1/3
5 superscript Start Fraction 1 over 3 End Fraction baseline

3^5
3 superscript 5 baseline

5^1

Answer 1

To rewrite \( 5 - \sqrt{3} \) using a rational exponent, we focus on the \(\sqrt{3}\) part. The square root of a number can be expressed as a rational exponent of \( \frac{1}{2} \). Therefore, we can rewrite \(\sqrt{3}\) as \( 3^{1/2} \).

Now, since the expression provided is \( 5 - \sqrt{3} \), it does not directly convert into a single exponent expression because it is a more complex expression involving the subtraction of a square root from a number.

However, if you're only considering the \(\sqrt{3}\) part, you would write it as \( 3^{1/2} \).

None of the responses directly match the original expression since \(5 - \sqrt{3}\) is not expressible as a singular rational exponent but for the \(\sqrt{3}\) the closest concept would be the following.

If you want the answer that corresponds with where a rational exponent connects with a root, you would choose:

**5^(1/3)** — though please note that this is not equivalent to \(5 - \sqrt{3}\) as the original expression.

If needing to choose based purely on context of rational exponent for \( \sqrt{3} \), please use:

**3^{5** (note this is just for '3' without relation to your expression). For clarity, it is necessary to denote that this wouldn't come from the original expression \( 5 - \sqrt{3} \).